Description Details Author(s) References See Also Examples
This package creates 2-level D-optimal designs with a user specified optimization function.
A design with non-zero D-efficiency can be used to estimate a model with all the main effects and all the two-factor interactions. The effect hierarchy assumption suggests that main effect estimation should be given more prominence than the estimation of two-factor interactions. The optimization functions in this package allow to user to create D-optimal designs that favor the main effect estimation over the estimation of two-factor interactions.
The main function in the package is Doptimize
. This function generates a single D-optimal design. The optimization function is specified using three parameters
α_1, α_2, α_3. The following
function is then optimized:
F = α_1 D + α_2 Ds + α_3 D1
Here D is the D-efficiency of the design. The Ds- and D1-efficiency are defined further below.
When specifying alpha_1=1, alpha_2=alpha_3=0 the function generates design that optimizes the D-efficiency. For values of alpha_2>0 the main effects are given more weight. This allows the user to create designs with good estimation of the main effects, while still allowing to estimate all 2-factor interactions.
The Ds- and D1-efficiency are defined as follows. For a design D the model matrix X can be split into [I X_1 X_2] with I the intercept, X_1 the main effects and X_2 the second order effects. We let X_{02}=[I X_2] and define D1=(|X_1^T X_1|)^{1/(k+1)}, Ds=(|X^T X|/|X_{02}^T X_{02} |)^{1/k} with k the number of factors of the design.
More details of the method and results of the the generation of optimal designs can be found the paper Eendebak (2015).
P.T. Eendebak <pieter.eendebak@gmail.com>
Alan Vazquez
Eendebak, P.T. and Schoen, E.D. (2015) Two-level designs to estimate all main effects and two-factor interactions, submitted to Technometrics
The documententation for Doptimize
and Defficiencies
.
For example code see the file example_Doptimize.R
or example_design_usage.R
included in the tests of the package.
1 | p = Doptimize(N=32, k=7, nrestarts=20, alpha1=1, alpha2=1, alpha3=0)
|
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